Method for predicting the mobility in mobile ad hoc networks

ABSTRACT

Disclosed are methods for determining the neighborhood local view of a mobile node in time which can facilitate the forwarding decision in the design of network protocols. In conventional mobile ad hoc networks nodes set up local topology view based on periodical received “Hello” messages. The conventional method is replaced with proactive and adaptive methods of predicting locations of nodes based on preserved historical information extracted from received “Hello” messages and constructing neighborhood view by aggregating predicted locations. This method is useful for providing updated and consistent topology local view that a network communication employs to determine optimal forward decisions and improve communication performance.

BACKGROUND

1. Technical Field

The invention relates generally to the communication of wireless LANsand more specifically to communication of mobile ad hoc networks. Stillmore specifically, the invention relates to methods of predicting themobility of mobile devices for constructing precise neighborhood localview in such networks.

2. Description of the Related Art

In most existing localized protocols for Mobile Ad hoc Networks(MANETs), each node emits “Hello” messages to advertise its presence andupdate its information. In periodical update, “Hello” intervals atdifferent nodes can be asynchronous to reduce message collision. Eachnode extracts its neighbors' information from latest received “Hello”messages to construct a local view of its neighborhood (e.g., 1-hoplocation information).

However, there are two main problems in that kind of neighborhood localview construction scheme. 1) Outdated local view: when we consider ageneral case where broadcasts or routing occur within “Hello” messageinterval while nodes move during that interval, forward decisions oflocalized protocols will be based on outdated neighborhood view; 2)Asynchronous local view: asynchronous sample frequency at each node,asynchronous “Hello” intervals in periodical update, and different“Hello” intervals in conditional update will cause asynchronousinformation for each neighbor in neighborhood local view.

Forward decisions based on outdated and asynchronous network topologyview may be inaccurate and hence cause delivery failure which can inducepoor coverage of broadcast task or route failures. If the dynamics ofthe network topology could be predicted in advance, appropriate forwarddecision can be made in order to avoid or reduce delivery failures.Neighborhood tracking is a task to determine the neighborhood local viewof a mobile node in time which can facilitate the forwarding decision innetwork protocols' design. Therefore, it could be of significance to thedesign of network protocols.

There exist two kinds of work which try to maintain accurate topologyview to assist the route path selection. First, in the work of Kim etal. (W.-I. Kim, D. H. Kwon, and Y.-J. Suh, “A reliable route selectionalgorithm using local positioning systems in mobile ad hoc networks,” InProceedings the IEEE International Conference on Communications,Amsterdam, USA, pp. 3191-3195, June, 2001.), a stable zone and a cautionzone of each node have been defined based on a node's position, speed,and direction information obtained from GPS. Specifically, a stable zoneis the area in which a mobile node can maintain a relatively stable linkwith its neighbor nodes since they are located close to each other. Acaution zone is the area in which a node can maintain an unstable linkwith its neighbor nodes since they are relatively far from each other.Second, Wu and Dai (J. Wu and F. Dai, “Mobility Control and ItsApplications in Mobile Ad Hoc Networks,” Accepted to appear in Handbookof Algorithms for Wireless Networking and Mobile Computing, A. Boukerche(ed.), Chapman & Hall/CRC, pp. 22-501-22-518, 2006.) have proposed aconservative “two transmission radius” method to compensate the outdatedtopology local view. However, all the above approaches are passive sincethey just try to compensate the inaccuracy of network topology viewrather than predict mobile nodes' positions to construct precise networktopology view in advance.

SUMMARY

The present invention achieves the foregoing features and results, aswell as others, by providing methods to predict the neighborhood ofmobile nodes in time in wireless ad hoc networks.

To address asynchronism problem, the present invention attaches thecurrent sending time into “Hello” messages. Nodes which receive “Hello”messages should include not only message contents but also receptiontime. By comparing reception time and sending time in “Hello” message,the time difference between two nodes can be calculated. To get asynchronized local view of any node S at any future time t, the presentinvention sets node S as the reference node and deduce its neighbor'ssynchronous time t′. To construct the updated neighborhood local view,piecewise linear and nonlinear prediction models are proposed which makeuse of a node's latest two or one information to predict its futurelocation. By aggregating predicted neighbors' location, node S canconstruct the updated and synchronous neighborhood view at actualtransmission time.

Using the methods of the invention, a dynamic approach can be made useof to construct predictive synchronized neighborhood local view when arouting or broadcasting task is triggered. Then the existing localizedprotocols can make forward decisions based on this updated local viewwhich can improve the performance of protocols.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart showing a method for predicting the mobility inmobile ad hoc networks according to a embodiment consistent with thepresent invention.

FIG. 2 is a analysis model for prediction interval according to aembodiment consistent with the present invention.

FIG. 3A is the sketch of location-based prediction model according to aembodiment consistent with the present invention.

FIG. 3B is the sketch of velocity-aided prediction model according to aembodiment consistent with the present invention.

FIG. 3C is the sketch of constant acceleration prediction modelaccording to a embodiment consistent with the present invention.

FIG. 4 is the function of smaller neighborhood range according to aembodiment consistent with the present invention.

FIG. 5 is analysis model for smaller neighborhood range according to aembodiment consistent with the present invention.

FIGS. 6A and 6B show examples of neighborhood tracking in periodicalupdate where the Z dimension coordinates according to a embodimentconsistent with the present invention.

DETAILED DESCRIPTION 1. Predictive and Synchronized NeighborhoodTracking Overview

Neighborhood tracking method flowchart of the present invention is shownin FIG. 1. In FIG. 1, method for predicting the mobility in mobile adhoc networks is illustrated. First step is constructing neighborhoodlocal view (S101). Next step is predicting locations of said node andits neighbor nodes at the same future time using said neighborhood localview (S103). Next step is updating neighborhood local view byaggregating neighbors' predicted location (S105). And next step isreconstructing said neighborhood local view by setting smallerneighborhood range (S107).

In FIG. 1, to address the asynchronous and outdated local view problem,the location of node S and the location of all its neighbor nodes arepredicted at the same future time t_(p) (with node S's clock) which isthe node S's actual emission time t_(b)+broadcast delay time t_(D). Bycollecting the predicted locations, node S can construct an updated andsynchronized neighborhood local view. The delay time t_(D) includes notonly the wireless network transmission delay t_(e) but also the packetand transmission processing time t_(s). t_(e) is basically fixed inwireless networks while t_(s) can vary according to packet size.

Moreover, the prediction interval is also affected by some other factorsand has a bound which we will analyze in next separate section. Howeverthere are still two issues: how to calculate neighbor nodes'corresponding prediction time and how to predict nodes' locations.

To calculate any neighbor node A's prediction time t′_(p), its timedifference to reference node S, t′_(d) is calculated. Thent′_(p)=t_(p)+t′_(d). To get t′_(d), local sending time t₁ and localreceived time t_(r) are included in “hello” messages. Then the timedifference between two nodes can be calculated ast′_(d)=t_(l)−t_(r)+t_(e) where t_(e) is the wireless networktransmission delay.

2. Analysis for Prediction Interval

When we schedule an actual transmission time for node S, if within theprediction interval, neighbor nodes already move out of the transmissionrange of node S, our prediction scheme will have no meaning. Thereforewe analyze the Transmission Range Dwell Time, T_(dwell), the time periodwithin which any neighbor node U stays in the transmission range of nodeS. R_(dwell) is the rate of crossing the boundary of its transmissionrange.

FIG. 2 shows an analytical model where we assume that node S moves witha velocity {right arrow over (V)}₁ and node U moves with a velocity{right arrow over (V)}₂. The relative velocity {right arrow over (V)} ofnode U to node S is given by

{right arrow over (V)}={right arrow over (V)} ₂ −{right arrow over (V)}₁   (1)

The magnitude of {right arrow over (V)} is given by

V=√{square root over (V ₁ ² +V ₂ ²−2V ₁ V ₂ cos(Φ₁−Φ₂))}  (2)

where V₁ and V₂ are the magnitudes of {right arrow over (V)}₁ and {rightarrow over (V)}₂, respectively. The mean value of V is given by

$\begin{matrix}{{{E\lbrack V\rbrack} = {\int_{V_{\min}}^{V_{\max}}{\int_{V_{\min}}^{V_{\max}}{\int_{0}^{2\pi}{\int_{0}^{2\pi}{\sqrt{u_{1}^{2} + u_{2}^{2} - {2u_{1}u_{2}{\cos \left( {\varphi_{1} - \varphi_{2}} \right)}}}{fv}_{1}}}}}}},v_{2},\Phi_{1},{{\Phi_{2}\left( {u_{1},u_{2},\varphi_{1},\varphi_{2}} \right)}\ {\varphi_{1}}\ {\varphi_{2}}\ {u_{1}}\ {u_{2}}}} & (3)\end{matrix}$

where f_(V) ₁ _(,V) ₂ _(Φ) ₁ _(,Φ) ₂ (v₁,v₂,φ₁,φ₂) is the joint pdf ofthe random variables V₁, V₂, Φ₁, Φ₂, V_(min) and V_(max) are the minimumand maximum moving speeds, the symbol E[V] is an average value of therandom variable V. Since the moving speeds V₁ and V₂ and directions Φ₁and Φ₂ of nodes S and U are independent, Eq. (3) can be simplified

$\begin{matrix}{{E\lbrack V\rbrack} = {\int_{V_{\min}}^{V_{\max}}{\int_{V_{\min}}^{V_{\max}}{\int_{0}^{2\pi}{\int_{0}^{2\pi}{\sqrt{\upsilon_{1}^{2} + \upsilon_{2}^{2} - {2\upsilon_{1}\upsilon_{2}{\cos \left( {\varphi_{1} - \varphi_{2}} \right)}}}{f_{V}\left( \upsilon_{1} \right)}{f_{V}\left( \upsilon_{2} \right)}{f_{\Phi}\left( \varphi_{1} \right)}{f_{\Phi}\left( \varphi_{2} \right)}{\varphi_{1}}\ {\varphi_{2}}\ {\upsilon_{1}}\ {\upsilon_{2}}}}}}}} & (4)\end{matrix}$

If Φ₁ and Φ₂ are uniformly distributed in (0, 2π), Eq. (4) can befurther rewritten as

$\begin{matrix}{{E\lbrack V\rbrack} = {\frac{1}{\pi^{2}}{\int_{V_{\min}}^{V_{\max}}{\int_{V_{\min}}^{V_{\max}}{\left( {\upsilon_{1} + \upsilon_{2}} \right){F_{e}\left( \frac{2\sqrt{\upsilon_{1}\upsilon_{2}}}{\upsilon_{1} + \upsilon_{2}} \right)}\ {f_{V}\left( \upsilon_{1} \right)}{f_{V}\left( \upsilon_{2} \right)}{\upsilon_{1}}\ {\upsilon_{2}}}}}}} & (5)\end{matrix}$

where

${F_{ɛ}(k)} = {\int_{0}^{1}{\sqrt{\frac{1 - {k^{2}t^{2}}}{1 - t^{2}}}\ {t}}}$

is complete elliptic integral of the second kind. Therefore, now we canconsider that node S is stationary, and node U is moving at a relativevelocity.

Assume that nodes are distributed uniformly and nodes' moving directionis distributed uniformly over [0, 2π], the mean value of R_(dwell) isgiven by

$\begin{matrix}{R_{dwell} = \frac{{E\lbrack V\rbrack}L}{\pi \; A}} & (6)\end{matrix}$

where A is the area of the transmission range and L is the perimeter ofthis area. Therefore

$\begin{matrix}{{E\left\lbrack T_{dwell} \right\rbrack} = \frac{\pi \; A}{{E\lbrack V\rbrack}L}} & (7)\end{matrix}$

In a word, our prediction interval should be bounded within the timeE[T_(dwell)].

3. Mobility Prediction

Camp et al. (T. Camp, J. Boleng and V. Davies, “A Survey of MobilityModels for Ad Hoc Network Research,” Wireless Comm. & Mobile Computing(WCMC), special issue on mobile ad hoc networking: research, trends andapplications, vol. 2, no. 5, pp. 483-502, 2002.) have given acomprehensive survey on mobility models for MANETs, from which we canfind that in some models nodes move linearly before changing direction.In the other models, they are not precisely linearly movement, nodesalso move linearly in a segment view.

Location-based Prediction: Suppose that there are two latest updates fora particular node respectively at time t_(1h) and t_(2h) (t_(1h)>t_(2h))with location information of (x_(1h), y_(1h), z_(1h)) and (x_(2h),y_(2h), z_(2h)). Assume at least within two successive update periodsthe node moves in a straight line with fixed speed as depicted in FIG.3A, we obtain

$\begin{matrix}\left\{ \begin{matrix}{\frac{x_{1h} - x_{2h}}{t_{1h} - t_{2h}} = \frac{x_{p} - x_{1h}}{t_{p} - t_{1h}}} \\{\frac{y_{1h} - y_{2h}}{t_{1h} - t_{2h}} = \frac{y_{p} - y_{1h}}{t_{p} - t_{1h}}} \\{\frac{z_{1h} - z_{2h}}{t_{1h} - t_{2h}} = \frac{z_{p} - z_{1h}}{t_{p} - t_{1h}}}\end{matrix} \right. & (8)\end{matrix}$

then the location (x_(p), y_(p), z_(p)) at a future time t_(p) can becalculated as

$\begin{matrix}\left\{ \begin{matrix}{x_{p} = {x_{1h} + {\frac{x_{1h} - x_{2h}}{t_{1h} - t_{2h}}\left( {t_{p} - t_{1h}} \right)}}} \\{y_{p} = {y_{1h} + {\frac{y_{1h} - y_{2h}}{t_{1h} - t_{2h}}\left( {t_{p} - t_{1h}} \right)}}} \\{z_{p} = {z_{1h} + {\frac{z_{1h} - z_{2h}}{t_{1h} - t_{2h}}{\left( {t_{p} - t_{1h}} \right).}}}}\end{matrix} \right. & (9)\end{matrix}$

In the conditional update, however, this model cannot be used becausethe latest update represents considerable changes compared to previousupdate.

Velocity-aided Prediction: Let (v′_(x), v′_(y), v′_(z)) be the velocityof its latest update for a particular node. Assume the node moves withthe speed within update period as depicted in FIG. 3B, the location(x_(p), y_(p), z_(p)) at a future time t_(p) can be calculated as

$\begin{matrix}\left\{ \begin{matrix}{x_{p} = {x_{1h} + {\upsilon_{x}^{\prime}\left( {t_{p} - t_{1h}} \right)}}} \\{y_{p} = {y_{1h} + {\upsilon_{y}^{\prime}\left( {t_{p} - t_{1h}} \right)}}} \\{z_{p} = {z_{1h} + {{\upsilon_{z}^{\prime}\left( {t_{p} - t_{1h}} \right)}.}}}\end{matrix} \right. & (10)\end{matrix}$

In high speed mobility networks we can assume the force on the movingnode is constant, that is, nodes move with constant acceleration.

Constant Acceleration Prediction: Let (v′_(x), v′_(y), v′_(z)) and(″_(x), v″_(y), v″_(z)) respectively be the velocity of those two updateas depicted in FIG. 3C. The principle of motion law are

V=v+at   (11)

and

$\begin{matrix}{S = {{{\upsilon \; t} + {\frac{1}{2}{at}^{2}}} = {{\overset{\_}{\upsilon}\; t} = {\frac{\upsilon + V}{2}t}}}} & (12)\end{matrix}$

where S is the displacement, v is the initial velocity and a is theacceleration during period t. We employ V denoting the final velocityafter period t.

Assume the fixed acceleration (a_(x), a_(y), a_(z)), and we apply aboveprinciple to X-dimension, we can obtain

$\begin{matrix}\left\{ \begin{matrix}{\upsilon_{x}^{\prime} = {\upsilon_{x}^{''} + {a_{x}\left( {t_{1h} - t_{2h}} \right)}}} \\{\upsilon_{x} = {\upsilon_{x}^{\prime} + {a_{x}\left( {t_{p} - t_{1h}} \right)}}} \\{{x_{p} - x_{1h}} = {\frac{\left( {\upsilon_{x}^{\prime} + \upsilon_{x}} \right)}{2}\left( {t_{p} - t_{1h}} \right)}}\end{matrix} \right. & (13)\end{matrix}$

Then we can get the expected location x_(p) as:

$\begin{matrix}{x_{p} = {x_{1h} + {\frac{{2\upsilon_{x}^{\prime}} + {\left( {\upsilon_{x}^{\prime} - \upsilon_{x}^{''}} \right)\frac{t_{p} - t_{1h}}{t_{1h} - t_{2h}}}}{2}\left( {t_{p} - t_{1h}} \right)}}} & (14)\end{matrix}$

Since Y and Z dimensions are the same with X-dimension, we obtain

$\begin{matrix}\left\{ \begin{matrix}{x_{p} = {x_{1h} + {\frac{{2\upsilon_{x}^{\prime}} + {\left( {\upsilon_{x}^{\prime} - \upsilon_{x}^{''}} \right)\frac{t_{p} - t_{1h}}{t_{1h} - t_{2h}}}}{2}\left( {t_{p} - t_{1h}} \right)}}} \\{y_{p} = {y_{1h} + {\frac{{2\upsilon_{y}^{\prime}} + {\left( {\upsilon_{y}^{\prime} - \upsilon_{y}^{''}} \right)\frac{t_{p} - t_{1h}}{t_{1h} - t_{2h}}}}{2}\left( {t_{p} - t_{1h}} \right)}}} \\{z_{p} = {z_{1h} + {\frac{{2\upsilon_{z}^{\prime}} + {\left( {\upsilon_{z}^{\prime} - \upsilon_{z}^{''}} \right)\frac{t_{p} - t_{1h}}{t_{1h} - t_{2h}}}}{2}{\left( {t_{p} - t_{1h}} \right).}}}}\end{matrix} \right. & (15)\end{matrix}$

Finally, by collecting predicted locations, we can construct an updatedand consistent neighborhood local view.

4. Enhancement Scheme

Inaccurate Local View: Although we provide a predictive and synchronizedsolution, however there exists another possible situation which cancause inaccurate local view. That is, a node S has not received a nodeU's latest update, so S neglects the existence of U. However U movesinto the node S's neighborhood during prediction time. FIG. 4( a) showsthe predicted local view of node S, where node U is not includedalthough it is the neighbor of S.

Smaller Neighborhood Range Scheme: In order to prevent the aforementioned problem, we propose how to reconstruct the neighborhood localview of S by applying smaller neighborhood radius (SR). By applying SRscheme, node S achieves smaller but accurate local view which is shownin FIG. 4( b).

Consider two nodes S and U as shown in FIG. 5. Node U is not within thetransmission range of node S at time t₀ and moves to position U′ at t₁.Assume that their distance at t₀ is d and U moves a distance of x withrespect to S at t₁. The probability that U enters into the transmissionrange of S is

$\begin{matrix}{{p\left( {x,d} \right)} = \left\{ \begin{matrix}{0\text{:}} & {x < {d - R_{1}}} \\{\frac{\varphi}{\pi}\text{:}} & {{d - R_{1}} \leq x \leq {d + R_{1}}} \\{0\text{:}} & {{x > {d + R_{1}}},}\end{matrix} \right.} & (16)\end{matrix}$

where

$\varphi = {\arccos\left( \frac{x^{2} + d^{2} - R_{1}^{2}}{2{xd}} \right)}$

is the largest value of □SUU′ that satisfies R₂<R₁. The probability thatany node moves into the transmission range of node S at t₁ is

$\begin{matrix}{{p(x)} = {\int_{R_{t}}^{\infty}{{p\left( {x,d} \right)}\ {d}}}} & (17)\end{matrix}$

The probability that a node with any relative speed v with respect to Smoves into its transmission range is

$\begin{matrix}{p = {\int_{0}^{2s}{{f_{\overset{\rightarrow}{V}}\ (v)}{p({fv})}{v}}}} & (18)\end{matrix}$

where {right arrow over (V)} is the random relative velocity vectorproposed in previous section and s is the maximum speed for any node.Recall, the direction of {right arrow over (V)} is also uniformlydistributed in [0, 2π] and is independent of the speed of {right arrowover (V)}. We know that □{right arrow over (V)}□ is uniformlydistributed in [0, 2π]. We calculate f_(□){right arrow over (V)}_(□) ata give time t as

$\begin{matrix}\begin{matrix}{{f_{\overset{\rightarrow}{V}}(t)} \approx \frac{{F_{\overset{\rightarrow}{V}}\left( \delta_{t} \right)} - {F_{\overset{\rightarrow}{V}}(t)}}{\delta_{t}}} \\{= \frac{P\left( {t \leq {\overset{\rightarrow}{V}} \leq {t + \delta_{t}}} \right)}{\delta_{t}}} \\{{= {\oint_{({0,0})}^{({{2\pi},s})}{\oint_{({0,0})}^{({{2\pi},s})}{{\frac{R\left( {{\overset{\rightarrow}{V}}_{2},{\overset{\rightarrow}{V}}_{1},t,{t + \delta_{t}}} \right)}{\left( {2\pi \; s} \right)^{2}\delta_{t}} \cdot {{\overset{\rightarrow}{V}}_{2}}}{{\overset{\rightarrow}{V}}_{1}}}}}},}\end{matrix} & (19)\end{matrix}$

where f_(□){right arrow over (V)}_(□(t)) is the distribution function,δ_(t) is a small positive value, and

$\begin{matrix}{{R\left( {{\overset{\rightarrow}{V}}_{2},{\overset{\rightarrow}{V}}_{1},a,b} \right)} = \left\{ \begin{matrix}{1\text{:}} & {a \leq {{{\overset{\rightarrow}{V}}_{2} - {\overset{\rightarrow}{V}}_{1}}} \leq b} \\{0\text{:}} & {{otherwise}.}\end{matrix} \right.} & (20)\end{matrix}$

Combining all above formulas, we can calculate the probability that anynode U moves into the transmission range of node S. Then, the expectedvalue of smaller neighborhood range (SR) can be given by

E[SR]=(1−p)R ₁   (21)

5. Simulation Results

We use ns-2.28 and its CMU wireless extension as simulation tool andassume AT&T's Wave LAN PCMCIA card as wireless node model withparameters as listed in Table 1. To demonstrate the comprehensiveeffectiveness of our proposal, we perform experiments in not only linear(Random Waypoint) but also nonlinear (Gauss-Markov) mobility modelswhich are widely used in simulating protocols designed for MANETs.

In neighborhood tracking, any node S is randomly chosen to predict itsneighbor nodes' locations for constructing local view. Local viewconstruction occurs within update interval. Table 2 displays oursimulation parameters.

TABLE 1 Parameters for wireless node model Parameters Value Frequency2.4 GHz Maximum transmission range 250 m MAC protocol 802.11 Propagationmodel free space/two ray ground

TABLE 2 Simulation parameters Parameters Value Simulation network size900 × 900 m² Mobile nodes speed range [0, 15] m/s Nodes number 50Simulation time 50 s Periodical update/check interval 2 s Predictioninterval 20 ms Reference distance of conditional update 1 m

The sample of predicted local view with velocity-based prediction underperiodical update is illustrated in FIG. 6 where the actual local viewand local view based on update information are also shown forcomparison. We can find that whatever in linear model or nonlinearmobile environment our predictive neighborhood views are almost the sameas actual neighborhoods while update info based views show obviousinaccuracy.

To evaluate the inaccuracy of local view, we define the metric ofposition error (PE) as the average distance difference betweenneighbors' actual positions and their positions in neighborhood view.For any node S suppose there are K neighbors (including S itself) in itsjth local view, and for any neighbor i let (x_(i), y_(i), z_(i))represent the actual location and (x′_(i), y′_(i), z′_(i)) be thelocation in local view, the PE_(j) for the jth neighborhood can becalculated as

$\begin{matrix}\sqrt{\frac{1}{K}{\sum\limits_{i = 1}^{K}\left\lbrack {\left( {x_{i}^{\prime} - x_{i}} \right)^{2} + \left( {y_{i}^{\prime} - y_{i}} \right)^{2} + \left( {z_{i}^{\prime} - z_{i}} \right)^{2}} \right\rbrack}} & (22)\end{matrix}$

Finally suppose we have W local views,

$\begin{matrix}{{PE} = {\frac{1}{W}{\sum\limits_{j = 1}^{W}{PE}_{j}}}} & (23)\end{matrix}$

The smaller the value of PE is, the more accurate the neighborhood localview is.

Table 3 and 4 show position error results under Random Waypoint andGauss-Markov models in our simulation. From above simulation results wecan demonstrate (1) both periodical and conditional update info basedview has more than three times inaccuracy compared with that of ourtracking schemes, which proves the necessary and effectiveness of ourproposition, (2) our schemes have very small prediction inaccuracy(especially in linear mobility environment), that is, they can preciselytrack neighborhood, (3) but different prediction models have differentperformance: velocity-aided scheme performs much better than other twomethods and the constant acceleration model does better thanlocation-based one, (4) in addition, the mobility model and updateprotocol also affects the performance of our scheme: under differentmobility models and update protocols the PE values are also different.

TABLE 3 PE under Random Waypoint model Records Type Prediction Scheme PEValue Periodical Update Info Based 7.258410 Update Location-based0.755039 Velocity-aided 0.003444 Constant Acceleration 0.261483Conditional Update Info Based 9.267584 Update Velocity-aided 0.000006Constant Acceleration 0.637606

TABLE 4 PE under Gauss-Markov Model Records Type Prediction Scheme PEValue Periodical Update Info Based 7.407275 Update Location-based2.281239 Velocity-aided 0.497334 Constant Acceleration 1.046533Conditional Update Info Based 9.497269 Update Velocity-aided 1.617758Constant Acceleration 2.813394

What has been described are preferred embodiments of the presentinvention. The foregoing description is intended to be exemplary and notlimiting in nature. Persons skilled in the art will appreciate thatvarious modifications and additions may be made while retaining thenovel and advantageous characteristics of the invention and withoutdeparting from this spirit. Accordingly, the scope of the invention isdefined solely by the appended claims as properly interpreted.

1. Method for predicting the mobility in mobile ad hoc networks, themethod comprising steps of: constructing neighborhood local view of anode; predicting locations of said node and its neighbor nodes at thesame future time using said neighborhood local view in prescribed timeinterval; updating neighborhood local view by aggregating neighbors'predicted location; reconstructing said neighborhood local view bysetting smaller neighborhood range.
 2. The method as claimed in claim 1,wherein the prescribed time interval is time period within which anyneighbor node stays in the transmission range of said node, T_(dwell) isgiven by${E\left\lbrack T_{dwell} \right\rbrack} = \frac{\pi \; A}{{E\lbrack V\rbrack}L}$where E[T_(dwell)] is average value of the T_(dwell), A is the area ofthe transmission range, L is the perimeter of this area, E[V] is averagevalue of V and V is relative velocity vector of node.
 3. The method asclaimed in claim 2, wherein average value of V, E[V] is given by${E\lbrack V\rbrack} = {\frac{1}{\pi^{2}}{\int_{V_{\min}}^{V_{\max}}{\int_{V_{\min}}^{V_{\max}}{\left( \ {v_{1} + v_{2}} \right){F_{e}\left( \frac{2\sqrt{v_{1}v_{2}}}{v_{1} + v_{2}} \right)}{f_{V}\left( v_{1} \right)}{f_{V}\left( v_{2} \right)}{v_{1}}\ {v_{2}}}}}}$where${F_{e}(k)} = {\int_{0}^{1}{\sqrt{\frac{1 - {k^{2}t^{2}}}{1 - t^{2}}}\ {t}}}$is complete elliptic integral of the second kind, fv(v1), fv(v2) is thejoint pdf of the random variables V1, V2.
 4. The method as claimed inclaim 1, wherein in said step of predicting locations of said node andits neighbor nodes, each location (x_(p), y_(p), z_(p)) at a future timet_(p) is calculated as $\left\{ \begin{matrix}{x_{p} = {x_{1h} + {\frac{x_{1h} - x_{2h}}{t_{1h} - t_{2h}}\left( {t_{p} - t_{1h}} \right)}}} \\{y_{p} = {y_{1h} + {\frac{y_{1h} - y_{2h}}{t_{1h} - t_{2h}}\left( {t_{p} - t_{1h}} \right)}}} \\{z_{p} = {z_{1h} + {\frac{z_{1h} - z_{2h}}{t_{1h} - t_{2h}}\left( {t_{p} - t_{1h}} \right)}}}\end{matrix}\quad \right.$ where (x_(1h), y_(1h), z_(1h)) is a locationat a time t_(1h), (x_(2h), y_(2h), z_(2h)) is a location at a timet_(2h), and t_(1h)>t_(2h).
 5. The method as claimed in claim 1, whereinin said step of predicting locations of said node and its neighbornodes, each location (x_(p), y_(p), z_(p)) at a future time t_(p) iscalculated as $\left\{ \begin{matrix}{x_{p} = {x_{1h} + {v_{x}^{\prime}\left( {t_{p} - t_{1h}} \right)}}} \\{y_{p} = {y_{1h} + {v_{y}^{\prime}\left( {t_{p} - t_{1h}} \right)}}} \\{z_{p} = {z_{1h} + {v_{z}^{\prime}\left( {t_{p} - t_{1h}} \right)}}}\end{matrix}\quad \right.$ where (x_(1h), y_(1h), z_(1h)) is a locationat a time t_(1h), (v′_(x), v′_(y), v′_(z)) is a velocity of latestupdate for a particular node.
 6. The method as claimed in claim 1,wherein in said step of predicting locations of said node and itsneighbor nodes, each location (x_(p), y_(p), z_(p)) at a future timet_(p) is calculated as $\left\{ \begin{matrix}{x_{p} = {x_{1h} + {\frac{{2v_{x}^{\prime}} + {\left( {v_{x}^{\prime} - v_{x}^{''}} \right)\frac{t_{p} - t_{1h}}{t_{1h} - t_{2h}}}}{2}\left( {t_{p} - t_{1h}} \right)}}} \\{y_{p} = {y_{1h} + {\frac{{2v_{y}^{\prime}} + {\left( {v_{y}^{\prime} - v_{y}^{''}} \right)\frac{t_{p} - t_{1h}}{t_{1h} - t_{2h}}}}{2}\left( {t_{p} - t_{1h}} \right)}}} \\{z_{p} = {z_{1h} + {\frac{{2v_{z}^{\prime}} + {\left( {v_{z}^{\prime} - v_{z}^{''}} \right)\frac{t_{p} - t_{1h}}{t_{1h} - t_{2h}}}}{2}\left( {t_{p} - t_{1h}} \right)}}}\end{matrix}\quad \right.$ where (x_(1h), y_(1h), z_(1h)) is a locationat a time t_(1h), (v′_(x), v′_(y), v′_(z)) is the velocity of firstupdate for a particular node, and (v−_(x), v″_(y), v″_(z)) is thevelocity of second update for a particular node.
 7. The method asclaimed in claim 1, wherein said smaller neighborhood range SR is givenbyE[SR]=(1−p)R ₁ where p is probability that any node moves into thetransmission range of node S, R₁ is radius of node S.
 8. The method asclaimed in claim 7, wherein${R\left( {{\overset{\rightarrow}{V}}_{2},{\overset{\rightarrow}{V}}_{1},a,b} \right)} = \left\{ \begin{matrix}{1\text{:}} & {a \leq {{{\overset{\rightarrow}{V}}_{2} - {\overset{\rightarrow}{V}}_{1}}} \leq b} \\{0\text{:}} & {{otherwise}.}\end{matrix} \right.$ where v is a relative speed, {right arrow over(V)} is the random relative velocity vector proposed in previous sectionand s is the maximum speed for any node.
 9. The method as claimed inclaim 8, wherein $\begin{matrix}{{f_{\overset{\rightarrow}{V}}(t)} \approx \frac{{F_{\overset{\rightarrow}{V}}\left( \delta_{t} \right)} - {F_{\overset{\rightarrow}{V}}(t)}}{\delta_{t}}} \\{= \frac{P\left( {t \leq {\overset{\rightarrow}{V}} \leq {t + \delta_{t}}} \right)}{\delta_{t}}} \\{{= {\oint_{({0,0})}^{({{2\pi},s})}{\oint_{({0,0})}^{({{2\pi},s})}{{\frac{R\left( {{\overset{\rightarrow}{V}}_{2},{\overset{\rightarrow}{V}}_{1},t,{t + \delta_{t}}} \right)}{\left( {2\pi \; s} \right)^{2}\delta_{t}} \cdot {{\overset{\rightarrow}{V}}_{2}}}{{\overset{\rightarrow}{V}}_{1}}}}}},}\end{matrix}$ where f_(□){right arrow over (V)}_(□(t)) is thedistribution function, δ_(t) is a small positive value, and$p = {\int_{0}^{2s}{{f_{\overset{\rightarrow}{V}}\ (v)}{p({fv})}{v}}}$